Pith Number

pith:L3M3WDMM

pith:2013:L3M3WDMMHMCBQUW3PGPZ7J2WKL

not attested not anchored not stored refs pending

Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps

Fr\'ed\'eric Faure (IF), Jean-Fran\c{c}ois Arnoldi (IF), Tobias Weich

arxiv:1302.3087 v2 · 2013-02-13 · math-ph · math.DS · math.MP · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L3M3WDMMHMCBQUW3PGPZ7J2WKL}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:30:26.122499Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ed9bb0d8c3b041852db799f9fa75652cfc4be9ee4cf650e14aadf45e7b72cbd

Aliases

arxiv: 1302.3087 · arxiv_version: 1302.3087v2 · doi: 10.48550/arxiv.1302.3087 · pith_short_12: L3M3WDMMHMCB · pith_short_16: L3M3WDMMHMCBQUW3 · pith_short_8: L3M3WDMM

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/L3M3WDMMHMCBQUW3PGPZ7J2WKL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 5ed9bb0d8c3b041852db799f9fa75652cfc4be9ee4cf650e14aadf45e7b72cbd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f3059f0c7a39a0c7f28350f102b56a23270bbf2d0ca1c44bbc26074eb048176",
    "cross_cats_sorted": [
      "math.DS",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-02-13T13:44:49Z",
    "title_canon_sha256": "8bb77f13b7acc1b4dc671c864fa7be40367bb2cd4591c66d5f534ffb3e938394"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.3087",
    "kind": "arxiv",
    "version": 2
  }
}